The experiments are carried out for different values of \(k^{*}\)  with
\(N=128\)  trajectories, each run for a total time \(T_{a}=\) 800 days.
Each experiment has thus a total computational cost of about 284 years.
The initial conditions of the trajectories are taken from the control
run, spaced by a few years from each other to ensure statistical independence.
The first 80 days of simulations are considered as a transient to
reach statistical equilibrium, and the statistical analysis is performed
on the last 720 days. The resampling time is set at 8 days, as in
[1]}. The choice of the resampling time is determined
by how trajectories starting from the same initial condition separate
in time after the addition of a small random perturbation. Heuristically
it is expected that a good choice should be \(\tau \)  to be of the order
of \(\tau _{c}\) . If the resampling time is much smaller than the autocorrelation
time of the process, the trajectories do not have time to separate
enough and useless resampling will increase the variance. If on the
contrary the resampling time is much larger than the autocorrelation
time, the trajectories will fall back to the typical states, and the
importance sampling efficiency will be lost. Tests with simpler systems
[2]} have shown that the precise value
of \(\tau \)  does not affect the results, as long as it is of the order
of the autocorrelation time. The trajectories are perturbed after
cloning by adding a small random field to the surface pressure, as
described in [1]}.
